Wittmann and Morgan on teaching quantum physics to non-science folks

Michael C. Wittmann and Jeffrey T. Morgan

Foregrounding epistemology and everyday intuitions in a quantum physics course for nonscience majors 

Phys. Rev. Phys. Educ. Res. 16, 020159 – Published 4 December 2020 

[This paper is part of the Focused Collection on Curriculum Development: Theory into Design.] In developing and modifying a course called Intuitive Quantum Physics for nonscience majors, several social and theoretical commitments informed our design decisions. We believed that the goal of a general education course should not be acquiring content knowledge alone, but more generally developing an approach to thinking scientifically. Thus, our course was designed to promote a deeper understanding of the nature of science through careful attention to students’ personal epistemologies. We emphasized everyday situations, be they social activities or personal experiences, as analogies to be used during instruction. We used these everyday events to help students make sense of quantum physics, choosing the topic exactly because it seems otherwise counterintuitive. Through this work, we hoped to help students make connections between complex topics (in this case in science) and their everyday experiences.

Barth-Cohen and Wittmann on Crosscutting Concepts as Concepts

Lauren Barth-Cohen and Michael C. Wittmann

Learning About Crosscutting Concepts as Concepts

Despite a growing interest in examining the learning processes involved in three-dimensional science learning, crosscutting concepts are an understudied dimension. We view crosscutting concepts as a type of concept. We argue that crosscutting concepts can be viewed as a kind of concept called a coordination class. We document two types of learning about crosscutting concepts. The first is focused on intuitions that provide a causal explanation, while the second focuses on coherent conceptual systems that are refined over time. In both cases there is an intertwined relationship between multiple crosscutting concepts, with some foregrounded or backgrounded. The results provide a new perspective on three-dimensional science learning that incorporates crosscutting concepts and relevant learning mechanisms.

Barth-Cohen, L. & Wittmann, M. (2020). Learning About Crosscutting Concepts as Concepts. In Gresalfi, M. and Horn, I. S. (Eds.), The Interdisciplinarity of the Learning Sciences, 14th International Conference of the Learning Sciences (ICLS) 2020, Volume 1 (pp. 557-560). Nashville, Tennessee: International Society of the Learning Sciences.

Wittmann Millay Alvarado Lucy Medina and Rogers on the resources framework and middle school students

Michael C. Wittmann, Laura A. Millay, Carolina Alvarado, Levi Lucy, Joshua Medina, Adam Rogers

Applying the resources framework of teaching and learning to issues in middle school physics instruction on energy

American Journal of Physics 87, 535 (2019); https://doi.org/10.1119/1.5110285

Our choice of model affects how we interpret what we observe. Students often have difficulties with the ideas of energy, but not all their difficulties are about energy, alone. We present two examples. In the first, student difficulties with mechanical energy seem to be with the system in which energy flows, not energy itself. In the second, students seem to use a substance metaphor of energy, which has been shown to be very productive, but use the “wrong” substance. Accounting for the nuances of student responses suggests the use of a model of knowledge and learning, the resources framework, that takes into account context dependence and the ways in which incorrect answers often contain substantial amounts of correct information.

Wittmann about the resources framework

Michael C. Wittmann

Research in the Resources Framework: Changing environments, consistent exploration

Wittmann, M.C. (2018). Research in the Resources Framework: Changing environments, consistent exploration. in Reviews in PER Volume 2: Getting Started in Physics Education Research, edited by C. Henderson and K. A. Harper (American Association of Physics Teachers, College Park, MD, 2018).

In this paper, I discuss my personal journey through one research tradition, that of the resources framework, and how it has evolved over time. In my present work, understanding learners' reasoning in physics in terms of the construction of large-scale models from small-scale resources emphasizes the person doing the constructing over the physics they are discussing. In this human-centered approach, I find value not in the correctness or incorrectness of a given response, but in the nature of construction, the individual's evaluation of their own ideas, and the communication between learners as they seek to understand each other. The resources framework has driven my attention toward a human-centered approach, and has had an effect on both my professional and personal life, in the process. In addition, events in my personal life have proven relevant to my professional work in ways that are reflected by my use of the resources framework to understand knowledge and learning.

Wittmann Rogers Alvarado Medina Millay on survey questions about energy

Using multiple survey questions about energy to uncover elements of middle school student reasoning

M. Wittmann, A. Rogers, C. Alvarado, J. Medina, and L. Millay

Physics Education Research Conference Proceedings 2017, Cincinnati, OH, 2017.

One power of middle school physics teaching is its focus on conceptual understanding, rather than mathematical modeling. Teaching energy in middle school allows one to focus on the conceptual ideas, metaphors, and analogies we use to make sense of the topic. In the Next Generation Science Standards, energy is both a core disciplinary idea in the physical sciences and a crosscutting concept. In this paper, we provide several examples of seeming contradictions in student responses to similar questions. For example, students think differently about energy flow to the air or the ground. They also think differently about energy flow in cold and hot situations, though not necessarily as expected. Analyzing these results carefully, in particular when comparing and contrasting seemingly similar questions, may help both researchers and teachers listen for ideas, target instruction, and recognize learning more effectively.

Physics Education Research Conference 2017
Part of the PER Conference series
Cincinnati, OH: July 26-27, 2017
Pages 440-443

DOI: 10.1119/perc.2017.pr.105

Wittmann, Alvarado, and Millay on teacher knowledge of energy

Michael C. Wittmann, Carolina Alvarado, Laura Millay

Teacher awareness of problematic facets of meaningful metaphors of energy

Latin American Journal of Physics Education 11, 2327 (2017).

English Abstract

How teachers respond to students depends, in part, on what they see in their students’ thinking. In a teacher professional development setting, we asked teachers to provide possible incorrect responses and explanations that students might give when discussing the gravitational potential energy of identical hikers walking to the summit of a mountain along different paths, from the same starting point. Teachers were aware of the common difficulties that students might have, including (1) energy is “used up” because of travel time, travel distance, or the effort exerted during travel (2) double-counting work and energy, and (3) energy being an intrinsic property of the hiker. Several of these difficulties use the metaphor of energy as a substance-like quantity, but teachers never made explicit that they were aware of the value of this metaphor in thinking about energy. We discuss the need for teachers to respond to multiple grain sizes of student thinking, including the metaphors they use and the different and at times problematic facets of each.

Keywords: Teacher training, Alternative conceptions, Gravity.

Resumen Espanol

La manera en que los maestros responden a los alumnos depende, en parte, de lo que ven en el pensamiento de los estudiantes. En un curso de capacitación, le pedimos a maestros que proporcionaran la posible respuesta incorrecta y la explicación de qué explicaciones podrían dar al analizar la energía gravitacional potencial de unos excursionistas idénticos caminando hacia la cumbre de una montaña por diferentes veredas, iniciando desde el mismo punto. Los maestros reconocían las dificultades comunes que los estudiantes podrían tener, incluyendo (1) la energía es “usada” en el tiempo viajado, distancia recorrida, o el esfuerzo requerido durante el viaje, (2) contar doblemente el trabajo y la energía, y (3) considerar la energía como una propiedad intrínseca del excursionista. Muchas de esas dificultades utilizan la metáfora de la energía como una cantidad del tipo sustancia, pero los maestros nunca hicieron explícito que ellos estaban al tanto del valor de dicha metáfora la pensar en energía. Discutimos la necesidad de los maestros a responder a las múltiples maneras de pensar de los estudiantes, incluyendo metáforas que usan así como las facetas que pueden ser problemáticas en ocasiones..

Palabras clave: Capacitación de maestros, Concepciones alternativas, Gravedad.

Link to journal: http://www.lajpe.org
Link to article: http://www.lajpe.org/jun17/2327_AAPT_2017.pdf

Barth-Cohen and Wittmann on coordination classes and energy

Lauren Barth-Cohen and Michael C. Wittmann

Aligning Coordination Class Theory With a New Context: Applying a Theory of Individual Learning to Group Learning

This article presents an empirical analysis of conceptual difficulties encountered and ways students made progress in learning at both individual and group levels in a classroom environment in which the students used an embodied modeling activity to make sense of a specific scientific scenario. The theoretical framework, coordination class theory, has primarily been used to capture individual learning in interview settings, and here it is applied to analytically capture both individual and group learning in a complex classroom environment. Classrooms of ninth-grade earth science students used the position of their bodies to model a specific scientific concept, the steady-state energy of the earth. The students encountered difficulties aligning their understanding of the scientific concept with the models. Subsequently, they changed their models in specific ways that better aligned their understanding of the scientific concept with their newly modified model. The theory is utilized to describe learning by both individuals and the group in this classroom environment and shows how a single student's contribution can dramatically affect the model and subsequent learning. Implications suggest new ways in which the theory may be useful for designing learning environments.

Schermerhorn and Thompson on symbolic forms and differential length elements

Benjamin P. Schermerhorn and John R. Thompson

Students’ use of symbolic forms when constructing differential length elements

As part of an effort to examine students' understanding of the structure of non-Cartesian coordinate systems and the differential vector elements associated with these systems, students in junior-level electricity and magnetism (E&M) were interviewed in pairs. Students constructed differential length and volume elements for an unconventional spherical coordinate system. A symbolic forms analysis found that students invoked known as well as novel symbolic forms when building these vector expressions. Further analysis suggests that student difficulties were primarily conceptual rather than symbolic.

B. P. Schermerhorn and J. R. Thompson, Students’ use of symbolic forms when constructing differential length elements, 2016 PERC Proceedings [Sacramento, CA, July 20-21, 2016], edited by D. L. Jones, L. Ding, and A. Traxler, doi:10.1119/perc.2016.pr.073.

Wittmann Alvarado Millay on facets and metaphors of teacher knowledge of student ideas

Michael C. Wittmann, Carolina Alvarado, and Laura A. Millay

Teachers' explanations of student difficulties with gravitational potential energy

In a teacher professional development meeting, teachers were asked a question about potential energy and then to discuss why students might give a particular response to it. Working together in a large group, they came up with responses and explanations that touched on multiple ways of thinking about energy and how these might affect student responses. We observed that teachers were aware of common metaphors for thinking about energy (like energy-as-a-substance) and that they gave multiple explanations for how students might have difficulties in applying these metaphors (e.g., energy is "used up" because of travel time, travel distance, or the effort exerted during travel). Additional explanations showed that teachers recognized how students might bring these ideas to the classroom. We discuss the need for teachers to respond to multiple grain sizes of student thinking, including the metaphors they use and the different facets of each. Assessments that help with this will be of greater value to teachers than the assessment we present.

M. C. Wittmann, C. Alvarado, and L. A. Millay, Teachers' explanations of student difficulties with gravitational potential energy, 2016 PERC Proceedings [Sacramento, CA, July 20-21, 2016], edited by D. L. Jones, L. Ding, and A. Traxler, doi:10.1119/perc.2016.pr.094.

Axthelm, Wittmann, Alvarado, and Millay on Idea Use Curves

Alex Axthelm, Michael C. Wittmann, Carolina Alvarado, and Laura Millay

Idea Use Curves

2015 Physics Education Research Conference Proceedings
Published Dec 18, 2015

Abstract.
A variety of tools have been created to understand student performance on multiple-choice tests, including analysis of normalized gain, item response curves, and more. These methods typically focus on correct answers. Many incorrect responses contain value and can be used as building blocks for instruction, but present tools do not account for productive reasoning leading to an incorrect response. Inspired by Item Response Curves, we introduce Idea Use Curves, which relate frequency with which an idea is used to student performance. We use this tool to consider ideas which may be present in both correct responses and distractors, letting us attend more to students’ conceptual understanding. This tool is made with the goal of identifying ideas that are consistently used by students who perform well or poorly, allowing researchers and instructors to look beyond the “correct/incorrect” paradigm. We explore student reasoning about energy as a proof of concept for this method.

Wittmann and Black on procedural resources in mathematics

Michael C. Wittmann and Katrina E. BLack

Mathematical actions as procedural resources: An example from the separation of variables.

Physical Review Special Topics - Physics Education Research, 11, 020114 - Published Sept 23, 2015
doi:10.1103/PhysRevSTPER.11.020114

Abstract:
[This paper is part of the Focused Collection on Upper Division Physics Courses.] Students learning to separate variables in order to solve a differential equation have multiple ways of correctly doing so. The procedures involved in separation include division or multiplication after properly grouping terms in an equation, moving terms (again, at times grouped) from one location on the page to another, or simply carrying out separation as a single act without showing any steps. We describe student use of these procedures in terms of Hammer’s resources, showing that each of the previously listed procedures is its own “piece” of a larger problem solving activity. Our data come from group examinations of students separating variables while solving an air resistance problem in an intermediate mechanics class. Through detailed analysis of four groups of students, we motivate that the mathematical procedures are resources and show the issues that students must resolve in order to successfully separate variables. We use this analysis to suggest ways in which new resources (such as separation) come to be.

Smith Wittmann Carter on analyzing the FMCE

Trevor I. Smith, Michael C. Wittmann, and Tom Carter

Applying model analysis to a resource-based analysis of the Force and Motion Conceptual Evaluation

Phys. Rev. ST Phys. Educ. Res 10, 020102 – Published 2 July 2014
DOI: http://dx.doi.org/10.1103/PhysRevSTPER.10.020102

ABSTRACT
Previously, we analyzed the Force and Motion Conceptual Evaluation in terms of a resources-based model that allows for clustering of questions so as to provide useful information on how students correctly or incorrectly reason about physics. In this paper, we apply model analysis to show that the associated model plots provide more information regarding the results of investigations using these question clusters than normalized gain graphs. We provide examples from two different institutions to show how the use of model analysis with our redefined clusters can provide previously hidden insight into the effectiveness of instruction.

Harrer PhD on productive resources in secondary school students' discourse about energy

Identifying Productive Resources in Secondary School Students' Discourse About Energy

Benedikt Walter Harrer

A growing program of research in science education acknowledges the beginnings of disciplinary reasoning in students’ ideas and seeks to inform instruction that responds productively to these disciplinary progenitors in the moment to foster their development into sophisticated scientific practice. This dissertation examines secondary school students’ ideas about energy for progenitors of disciplinary knowledge and practice. Previously, researchers argued that students’ ideas about energy were constrained by stable and coherent conceptual structures that conflicted with an assumed unified scientific conception and therefore needed to be replaced. These researchers did not attend to the productive elements in students’ ideas about energy.
To analyze the disciplinary substance in students’ ideas, a theoretical perspective was developed that extends Hammer and colleagues’ resources framework. This elaboration allows for the identification of disciplinary productive resources—i.e., appropriately activated declarative and procedural pieces of knowledge—in individual students’ utterances as well as in the interactions of multiple learners engaged in group learning activities.

Using this framework, original interview transcripts from one of the most influential studies of students’ ideas about energy (Watts, 1983. Some alternative views of energy. Physics Education, 18/5, 213-217) were analyzed. Disciplinary productive resources regarding the ontology of energy, indicators for energy, and mechanistic reasoning about energy were found to be activated by interviewed students. These valuable aspects were not recognized by the original author. An interpretive analysis of video recorded student-centered discourse in rural Maine middle schools was carried out to find cases of resource activation in classroom discussions. Several cases of disciplinary productive resources regarding the nature of energy and its forms as well as the construction of a mechanistic energy story were identified and richly described.

Like energy, resources are manifested in various ways. The results of this study imply the necessity of appropriate disciplinary training for teachers that enables them to recognize and productively respond to disciplinary progenitors of the energy concept in students’ ideas.

Recommended Citation:

Harrer, Benedikt Walter, "Identifying Productive Resources in Secondary School Students' Discourse About Energy" (2013). Electronic Theses and Dissertations. 2065.
https://digitalcommons.library.umaine.edu/etd/2065

Harrer, Flood, and Wittmann on productive resources about energy

Benedikt W. Harrer, Virginia J. Flood, and Michael C. Wittmann

Productive resources in students’ ideas about energy: An alternative analysis of Watts’ original interview transcripts
Phys. Rev. ST Phys. Educ. Res. 9, 023101 – Published 10 September 2013

For over 30 years, researchers have investigated students’ ideas about energy with the intent of reforming instructional practice. In this pursuit, Watts contributed an influential study with his 1983 paper “Some alternative views of energy” [Phys. Educ. 18, 213 (1983)]. Watts’ “alternative frameworks” continue to be used for categorizing students’ non-normative ideas about energy. Using a resources framework, we propose an alternate analysis of student responses from Watts’ interviews. In our analysis, we show how students’ activated resources about energy are disciplinarily productive. We suggest that fostering seeds of scientific understandings in students’ ideas about energy may play an important role in their development of scientific literacy.

Wittmann on conceptual blending in wave propagation

Michael C. Wittmann
Using conceptual blending to describe emergent meaning in wave propagation
Proceedings of the 2010 International Conference on the Learning Sciences

Students in interviews on a wave physics topic give answers through embodied actions which connect their understanding of the physics to other common experiences. When answering a question about wavepulses propagating along a long taut spring, students' gestures help them recruit information about balls thrown the air. I analyze gestural, perceptual, and verbal information gathered using videotaped interviews and classroom interactions. I use conceptual blending to describe how different elements combine to create new, emergent meaning for the students and compare this to a knowledge-in-pieces approach.

Black and Wittmann on Resource Creation in Mechanics

Katrina E. Black and Michael C. Wittmann
Procedural Resource Creation in Intermediate Mechanics
AIP Conf. Proc. -- November 5, 2009 -- Volume 1179, pp. 97-101
2009 PHYSICS EDUCATION RESEARCH CONFERENCE

A problem in resource theory is describing the creation of new, high-level resources. We model resource creation by analyzing four student groups separating variables in a group quiz setting. The task was to solve an air resistance problem with uncommon initial conditions. We assess the fluency of each group and two observables: use of overt (such as divide, subtract, equals) and covert (such as moving, bringing, or pulling over) mathematical and use of accompanying gestures (such as circling, grabbing, or sliding). For each group, the type of language and gesture used corresponds to how easily they carry out separation of variables. We create resource graphs for each group to organize our observations and use these graphs to model the creation of the procedural resource Separate Variables.

Sayre Wittmann on resource plasticity and coordinate systems

Eleanor C. Sayre, Michael C. Wittmann

Plasticity of intermediate mechanics students’ coordinate system choice
Phys. Rev. ST Phys. Educ. Res. 4, 020105 (2008)

We investigate the interplay between mathematics and physics resources in intermediate mechanics students. In the mechanics course, the selection and application of coordinate systems is a consistent thread. At the University of Maine, students often start the course with a strong preference to use Cartesian coordinates, in accordance with their prior physics and mathematics classes. In small-group interviews and in homework help sessions, we ask students to define a coordinate system and set up the equations of motion for a simple pendulum for which polar coordinates are more appropriate. We analyze video data from several encounters using a combination of Process/Object theory and Resource Theory. We find that students sometimes persist in using an inappropriate Cartesian system. Furthermore, students often derive (rather than recall) the details of the polar coordinate system, indicating that their knowledge is far from solid. To describe our work more precisely, we define a scale of plasticity and several heuristics for defining resources and their plasticity.

Smith and Wittmann on a resources analysis of the FMCE

Trevor I. Smith and Michael C. Wittmann

Applying a resources framework to analysis of the Force and Motion Conceptual Evaluation
Phys. Rev. ST Phys. Educ. Res. 4, 020101 (2008) [12 pages]

We suggest one redefinition of common clusters of questions used to analyze student responses on the Force and Motion Conceptual Evaluation. Our goal is to propose a methodology that moves beyond an analysis of student learning defined by correct responses, either on the overall test or on clusters of questions defined solely by content. We use the resources framework theory of learning to define clusters within this experimental test that was designed without the resources framework in mind. We take special note of the contextual and representational dependence of questions with seemingly similar physics content. We analyze clusters in ways that allow the most common incorrect answers to give as much, or more, information as the correctness of responses in that cluster. We show that false positives can be found, especially on questions dealing with Newton’s third law. We apply our clustering to a small set of data to illustrate the value of comparing students’ incorrect responses which are otherwise identical on a correct or incorrect analysis. Our work provides a connection between theory and experiment in the area of survey design and the resources framework.

Originally posted at arxiv.org, where a pre-print remains available.

Sayre Ph.D.: Resource justification and development

Eleanor C. Sayre,
Plasticity: Resource Justification and Development
Unpublished Ph.D. dissertation, University of Maine, 2007

Physics education research is fundamentally concerned with understanding the processes of student learning and facilitating the development of student understanding. A better understanding of learning processes and outcomes is integral to improving said learning. In this thesis, I detail and expand upon Resource Theory, allowing it to account for the development of resources and connecting the activation and use of resources to experimental data. Resource Theory is a general knowledge-in-pieces schema theory. It bridges cognitive science and education research to describe the phenomenology of problem solving. Resources are small, reusable pieces of thought that make up concepts and arguments. The physical context and cognitive state of the user determine which resources are available to be activated; different people have different resources about different things. Over time, resources may develop, acquiring new meanings as they activate in different situations. In this thesis, I introduce "plasticity," a continuum for describing the development of resources. The plasticity continuum blends elements of Process/Object and Cognitive Science with Resource Theory. The name evokes brain plasticity and myelination (markers of learning power and reasoning speed, respectively) and materials plasticity and solidity (with their attendant properties, deformabihty and stability). In the plasticity continuum, the two directions are more plastic and more solid. More solid resources are more durable and more connected to other resources. Users tend to be more committed to them because reasoning with them has been fruitful in the past. Similarly, users tend not to perform consistency checks on them any more. In contrast, more plastic resources need to be tested against the existing network more often, as users forge links between them and other resources. To explore these expansions and their application, I present several extended examples drawn from an Intermediate Mechanics class. The first extended example comes from damped harmonic motion; the others discuss coordinate system choice for simple pendula. In every case, the richness of student reasoning indicates that a wealth of resources of varying plasticity are in play. To analyze the encounters, a careful and fine-grained theoretical approach is required.

Recommended Citation

Sayre, Eleanor C., "Plasticity: Resource Justification and Development" (2007). Electronic Theses and Dissertations. 1107.
http://digitalcommons.library.umaine.edu/etd/1107

Black and Wittmann on the epistemic games in integration

K.E. Black and M.C. Wittmann
Epistemic Games in Integration: Modeling Resource Choice
Physics Education Research Conference Proceedings 2007.

As part of an ongoing project to understand how mathematics is used in advanced physics to guide one's conceptual understanding of physics, we focus on students' interpretation and use of boundary and initial conditions when solving integrals. We discuss an interaction between two students working on a group quiz problem. After describing the interaction, we briefly discuss the procedural resources that we use to model the students' solutions. We then use the procedural resources introduced earlier to draw resources graphs describing the two epistemic game facets used by the students in our transcript. ©2007 American Institute of Physics

AIP Conf. Proc. -- November 12, 2007 -- Volume 951, pp. 53-56
2007 PHYSICS EDUCATION RESEARCH CONFERENCE; DOI:10.1063/1.2820945